# Antimodular actions of non-amenable groups

#### by Inessa Epstein

Institution: University of California, Los Angeles
Date: Wed 28th March 2007
Time: 4:30 PM
Location: Room 107, Richard Berry Building

Abstract: Consider a countable infinite group G which acts in a Borel way on a standard Borel space X. This gives rise to a Borel orbit equivalence relation with countable equivalence classes. It is of interest to classify such actions in terms of orbit equivalence and to compare them in terms of
Borel reducibility. Call a group action on a standard Borel space modular if there exists a sequence of countable Borel partitions, each refining the previous, that separate points and are invariant under the action. We
present actions of countable, non-amenable groups that are antimodular and discuss applications to orbit equivalence.